How does papal authority differ from scientific authority?

“The authority of science, which is recognized by most philosophers of the modern epoch, is a very different thing from the authority of the Church, since it is intellectual, not governmental. No penalties fall upon those who reject it; no prudential arguments influence those who accept it. It prevails solely by its intrinsic appeal to reason. It is, moreover, a piecemeal and partial authority; it does not, like the body of Catholic dogma, lay down a complete system, covering human morality, human hopes, and the past and future history of the universe. It pronounces only on whatever, at the time, appears to have been scientifically ascertained, which is a small island in an ocean of nescience. There is yet another difference from ecclesiastical authority, which declares its pronouncements to be absolutely certain and eternally unalterable: the pronouncements of science are made tentatively, on a basis of probability, and are regarded as liable to modification. This produces a temper of mind very different from that of the medieval dogmatist.“

— Bertrand Russell, A History of Western Philosophy (1945), Book Three. Modern Philosophy, Part I. From the Renaissance to Hume, Ch. I: General Characteristics, p. 432

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Image: Detail from the Ghent Altarpiece (1420-1432) showing three popes (Martin V, Gregory VII, and Antipope Alexander V) and other bishops illustrating what is understood today as the “magisterium” of the Catholic Church. The Magisterium is the church\'s authority or office to give authentic interpretation of the word of God. The concept of papal infallibility developed in the late Middle Ages, but a definitive statement and explanation of these doctrines did not occur until the 19th century at the First Vatican Council (1869-1870). Half a century later, Pope Pius XII (reigned 1939-1958) authoritatively proclaimed the scope of the Magisterium further, stating that the faithful must be obedient to even the ordinary Magisterium of the Pope and that “there can no longer be any question of free discussion between theologians” once the Pope has spoken on any given issue.